DOCSLIB.ORG

Yakov Petrovich Terletskii (1912‒1993)

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Yakov Petrovich Terletskii (1912‒1993) 134 Hiroshi ICHIKAWA Materialist Perestroika of Quantum Dynamics and Soviet Ideology: Yakov Petrovich Terletskii (1912‒1993) Hiroshi ICHIKAWA* Abstract Yakov Petrovich Terletskii (1912‒1993), a professor in theoretical physics at Moscow State University wrote extensively on the “philosophical” issues of modern physics, particularly in the first half of the 1950s. Outside Russia, his name is rarely mentioned. Nevertheless, it is likely that he has been regarded as a “cat’s-paw” of the ideological apparatus of the Marxist state. May we share such a view even now, in spite of the major changes in the historiography of Soviet science we have already seen in the last few decades? Thanks to the progress of the study based on formerly classified documents in various Russian archives, we see that the totalitarian model that had been applied to the understanding of Soviet society for a long time rapidly lost its popularity and was replaced with a more pluralistic view. This study reexamines and reevaluates the thoughts and activities of Yakov Terletskii from the viewpoint of today’s understanding of the historiography of Soviet science. It provides a new analysis, connecting the global quest of physicists for a new approach to quantum dynamics to the local context particular to the Soviet Union. Keywords: Yakov Terletskii, Modern Physics, Quantum Dynamics, the Copenhagen Interpretation, the Soviet Union, Ideology, Dialectical Materialism. Robespierrists! Anti-Robespierrists! For pity’s sake, simply tell us what Robespierre was. [Marc Bloch, The Historian’s Craft. trans. by Peter Putnam (Manchester: Manchester University Press, 1954), p. 140.] 1. Introduction Independently from Ethan Pollock,1 the author of this paper has taken notice of the consequences of an ideologically charged campaign under the guise of a series of academic “discussions” initiated in various fields of science in Postwar Soviet Union, as * Professor at the Graduate School of Integrated Arts and Sciences, Hiroshima University. 1‒7‒1, Kagami-yama, Higashi-Hiroshima 739‒8521, Japan. E-mail: [email protected] This paper is a revised and expanded version of a paper that the author published in Japanese; ICHIKAWA Hisroshi, “Yakovu Teruretsukii wo go-Zonji desu-ka? (Do you know Yakov Terletskii?),” Arena, vol. 20 (2017), 51‒66. The author thanks Prof. Vladimir Pavlovich Vizgin, Prof. Chieko Kojima, Prof. Kôji Kanayama, and Mr. Nobumichi Ariga for their assistances and useful advices. 1 Ethan Pollock, Stalin and the Soviet Science Wars (Princeton: Princeton University Press, 2006). HISTORIA SCIENTIARUM Vol. 28‒2 (2019) Materialist Perestroika of Quantum Dynamics and Soviet Ideology 135 one of the important opportunity for the cultivation of “the Cold War climate” among Soviet physicists that objectively drove them to Cold War scientific and technological projects such as nuclear weapon development.2 Soon after this “discussion” began in the field of philosophy in 1947, and then subsequently in the field of physics, Vladimir Kessenikh (1903‒1970), Vasilii Nozdryov (1913‒1995), and several other professors and teachers at the Faculty of Physics (Fizicheskii fakul’tet; Fizfak) of the Moscow State University (MSU), who called themselves “patriotic and materialistic physicists,” launched an attack on leading physicists such as Grigorii Landsberg (1890‒1957), Pyotr Kapitsa (1894‒1984, a Nobel Prize laureate in 1978), and Igor Tamm (1895‒1971, a Nobel Prize laureate in 1958), condemning them for their “idealism” and “cosmopolitanism or worship of foreign science.”3 What is astonishing here for the historians of science, especially of modern physics, is the fact that the physicists themselves, neither the philosophers nor the Party ideologues, criticized quantum dynamics for its “idealist distortion” of physics. However, could there have been any genuine physicists who were indifferent to quantum dynamics and the principle of relativity by the second half of the 1940s? Indeed, some “patriotic and materialistic physicists” only outwardly condemned “idealism” in physics.4 Nevertheless, their criticism against the “idealist” nature of quantum dynamics was so heated that the exchange of words between them and the modern physicists they were accusing presented itself as “a kangaroo court.” Among such accusers, Yakov Petrovich Terletskii (1912‒1993), a professor at MSU in charge of theoretical physics, who produced a number of “philosophical” papers on modern physics,5 attracts our attention. Although he 2 Ichikawa, Hiroshi, Reisen to Kagaku-Gijutsu: Sorenpô 1945‒1955 (The Cold War, Science and Technology: The Soviet Union, 1945‒1955) (Kyoto: Minerva Shobô, 2007). See Chapter 2 in this book (99‒ 153): Here, Ichikawa demonstrates that the social background of this dispute was rooted in the jealousy and antagonism of a group of physicists against another group of physicists, which accumulated due to distortion in the Soviet academic regime before and during the war. In spite of that, the initiators had no further intentions other than ideological restraint and unification in the occasion of the outbreak of the Cold War. A large-scale “academic discussion” campaign beginning in 1947 with “the philosophical dispute” explosively released these complaints in ideological terms from some groups of scientists in a warped form. 3 V.P. Vizgin, “Yadernyi shchit v “tridtsatiletnei voine” fizikov s nevezhestvennoi kritikoi sovremennykh fizicheskikh teorii,” Uspekhi Fizicheskikh Nauk, vol. 169 (1999): p. 1372. 4 For example, Sergei Vasil’ev (1904‒1999), a professor at MSU and supporter of the “patriotic and materialistic physicists” in postwar academic “discussions,” was in turn rebuked by the dean of the Faculty of Chemistry of MSU for his “double-dealing” attitude towards “idealistic” physical theories. Even while he outwardly condemned “idealism” in physics, he taught students the “idealistic” theories of Niels Bohr (1885‒ 1962), Ernest Rutherford (1871‒1937), Linus Pauling (1901‒1994), and Erwin Schrödinger (1887‒1961) in his lectures. [Rossiiskii gosudarstvennyi arkhiv sotsal’no-politicheskoi istorii (RGASPI). Fond (F.). 17, Opis’ (Op.). 125, Delo (D.) 618. 176] 5 Except for works categorized as “commentary,” from 1948 to 1956 he published six articles for the journal, Voprosy Filosofii; (1) Ya.P. Terletskiy, “Zamechanie v diskussii o prirode fizicheskogo znaniya: Obsuzhdeniye stat’i M.A. Markova (Remark in the Discussion on the Nature of the Knowledge of Physics: The Discussion on the Paper by M.A. Markov),” Voprosy Filosofii, no. 3 (1948), 228‒231; (2) Ya.P. Terletskiy, “Problemy razvitiya kvantovoi teorii (Problems of the Development of Quantum Theory),” Voprosy Filosofii, 136 Hiroshi ICHIKAWA was an able physicist, it would be hard to argue that his name is well known. In any historiography of modern physics, we have difficulty in finding his name6 except within the works written in Russian.7 However, Max Jammer’s well-received work on the history and philosophy of quantum dynamics is comprehensive enough to mention Terletskii. His name is cited when Jammer refers to the early responses to the idea of a young American physicist, David Bohm (1917‒92), who proposed a new approach to quantum dynamics (which I will discuss below). Terletskii was one of the first physicists to express his approval of Bohm’s idea. Jammer states, “It is therefore not surprising that first favorable criticism of Bohm’s idea came from those sources who for one reason or another sympathized with such ideological consideration.”8 As seen here, the thoughts and activities of Terletskii were associated with Soviet ideology. Is such an interpretation still correct? In this study, by rereading the work of Terletskii, examining newly declassified documents and reviewing other materials, the author reexamines the thought and activities of Terletskii, who is apt to be assigned the role of a villain in the Soviet history of physics. 2. Life and Activities of Yakov Terletskii To commemorate his 60th birthday, an article reviewing his career and academic contributions was issued in a bulletin, Istoriya i Metodologiya Estestvennykh Nauk (History no. 5 (1951), 51‒61; (3) Ya.P. Terletskiy, “Ob odnoy iz knig akademika L.D. Landau i ego uchenikov (On One of the Books of Academician L.D. Landau and his Students),” ibid., 190‒194; (4) Ya.P. Terletskiy, “O soderzhanii sovremennoi fizicheskoi teorii prostranstva i vremeni (On the Content of the Modern Physical Theory of Space and Time),” Voprosy Filosofii, no. 3 (1952), 191‒197; (5) Ya.P. Terletskiy, “Ob izlozhenii osnov spetsial’noi teorii otnositel’nosti (On the Presentation of the Foundations of the Special Theory of Relativity),” Voprosy Filosofii, no. 4 (1953), 207‒212; (6) Ya.P. Terletskiy, “O vzaimoprevrashchayemosti elementarnykh chastits (On the Interconversion of Elementary Particles),” Voprosy Filosofii, no. 2 (1956), 164‒166. 6 For example, even Alexei Kojevnikov, who published a political and social history of Soviet physics, refers to his name only in the connection of the so-called “Copenhagen Mission” case (which I mention below) in which in 1945 Terletskii was dispatched to Copenhagen to obtain information on nuclear weapon development. See Alexei Kojevnikov, Stalin’s Great Science: The Times and Adventures of Soviet Physicists (London: Imperial College Press, 2004), pp. 149‒150. Slava Gerovitch, who attracted a lot of interest because of his fresh approach to the history of Soviet science, refers to the name of Terletskii in connection with his dismissal from the editorial board
Load more

Recommended publications
  • From Time Series to Stochastics: a Theoretical Framework with Applications on Time Scales Spanning from Microseconds to Megayears
    Orlob International Symposium 2016 University California Davis 20-21 June 2016 From time series to stochastics: A theoretical framework with applications on time scales spanning from microseconds to megayears Demetris Koutsoyiannis & Panayiotis Dimitriadis Department of Water Resources and Environmental Engineering School of Civil Engineering National Technical University of Athens, Greece ([email protected], http://www.itia.ntua.gr/dk/) Presentation available online: http://www.itia.ntua.gr/en/docinfo/1618/ Part 1: On names and definitions D. Koutsoyiannis & P. Dimitriadis, From time series to stochastics 1 Schools on names and definitions The poetic school What’s in a name? That which we call a rose, By any other name would smell as sweet. —William Shakespeare, “Romeo and Juliet” (Act 2, scene 2) The philosophico-epistemic school Ἀρχή σοφίας ὀνομάτων ἐπίσκεψις (The beginning of wisdom is the visiting (inspection) of names) ―Attributed to Antisthenes of Athens, founder of Cynic philosophy Ἀρχὴ παιδεύσεως ἡ τῶν ὀνομάτων ἐπίσκεψις” (The beginning of education is the inspection of names) ―Attributed to Socrates by Epictetus, Discourses, Ι.17,12, The beginning of wisdom is to call things by their proper name. ―Chinese proverb paraphrasing Confucius’s quote “If names be not correct, language is not in accordance with the truth of things.” D. Koutsoyiannis & P. Dimitriadis, From time series to stochastics 2 On names and definitions (contd.) The philosophico-epistemic school (contd.) When I name an object with a word, I thereby assert its existence.” —Andrei Bely, symbolist poet and former mathematics student of Dmitri Egorov, in his essay “The Magic of Words” “Nommer, c’est avoir individu” (to name is to have individuality).
    [Show full text]
  • Biography of N. N. Luzin
    BIOGRAPHY OF N. N. LUZIN http://theor.jinr.ru/~kuzemsky/Luzinbio.html BIOGRAPHY OF N. N. LUZIN (1883-1950) born December 09, 1883, Irkutsk, Russia. died January 28, 1950, Moscow, Russia. Biographic Data of N. N. Luzin: Nikolai Nikolaevich Luzin (also spelled Lusin; Russian: НиколайНиколаевич Лузин) was a Soviet/Russian mathematician known for his work in descriptive set theory and aspects of mathematical analysis with strong connections to point-set topology. He was the co-founder of "Luzitania" (together with professor Dimitrii Egorov), a close group of young Moscow mathematicians of the first half of the 1920s. This group consisted of the higly talented and enthusiastic members which form later the core of the famous Moscow school of mathematics. They adopted his set-theoretic orientation, and went on to apply it in other areas of mathematics. Luzin started studying mathematics in 1901 at Moscow University, where his advisor was professor Dimitrii Egorov (1869-1931). Professor Dimitrii Fedorovihch Egorov was a great scientist and talented teacher; in addition he was a person of very high moral principles. He was a Russian and Soviet mathematician known for significant contributions to the areas of differential geometry and mathematical analysis. Egorov was devoted and openly practicized member of Russian Orthodox Church and active parish worker. This activity was the reason of his conflicts with Soviet authorities after 1917 and finally led him to arrest and exile to Kazan (1930) where he died from heavy cancer. From 1910 to 1914 Luzin studied at Gottingen, where he was influenced by Edmund Landau. He then returned to Moscow and received his Ph.D.
    [Show full text]
  • Notes on the Poisson Point Process
    Notes on the Poisson point process Paul Keeler January 5, 2016 This work is licensed under a “CC BY-SA 3.0” license. Abstract The Poisson point process is a type of random object known as a point pro- cess that has been the focus of much study and application. This survey aims to give an accessible but detailed account of the Poisson point process by covering its history, mathematical definitions in a number of settings, and key properties as well detailing various terminology and applications of the process, with rec- ommendations for further reading. 1 Introduction In probability, statistics and related fields, a Poisson point process or a Poisson process or a Poisson point field is a type of random object known as a point pro- cess or point field that consists of randomly positioned points located on some underlying mathematical space [68]. The process has convenient mathematical properties [39], which has led to it being frequently defined in Euclidean space and used as a mathematical model for seemingly random processes in numer- ous disciplines such as astronomy [5], biology [53], ecology [70], geology [16], physics [61], image processing [12], and telecommunications [7][28]. The Poisson point process is often defined on the real line playing an impor- tant role in the field of queueing theory [40] where it is used to model certain random events happening in time such as the arrival of customers at a store or phone calls at an exchange. In the plane, the point process, also known as a spa- tial Poisson process [9], may represent scattered objects such as users in a wireless network [2, 6, 7, 27], particles colliding into a detector, or trees in a forest [68].
    [Show full text]
  • MATH 590: Meshfree Methods Chapter 1 — Part 1: Introduction and a Historical Overview
    MATH 590: Meshfree Methods Chapter 1 — Part 1: Introduction and a Historical Overview Greg Fasshauer Department of Applied Mathematics Illinois Institute of Technology Fall 2014 [email protected] MATH 590 – Chapter 1 1 Outline 1 Introduction 2 Some Historical Remarks [email protected] MATH 590 – Chapter 1 2 Introduction Outline 1 Introduction 2 Some Historical Remarks [email protected] MATH 590 – Chapter 1 3 Introduction General Meshfree Methods Meshfree Methods have gained much attention in recent years interdisciplinary field many traditional numerical methods (finite differences, finite elements or finite volumes) have trouble with high-dimensional problems meshfree methods can often handle changes in the geometry of the domain of interest (e.g., free surfaces, moving particles and large deformations) better independence from a mesh is a great advantage since mesh generation is one of the most time consuming parts of any mesh-based numerical simulation new generation of numerical tools [email protected] MATH 590 – Chapter 1 4 Introduction General Meshfree Methods Applications Original applications were in geodesy, geophysics, mapping, or meteorology Later, many other application areas numerical solution of PDEs in many engineering applications, computer graphics, optics, artificial intelligence, machine learning or statistical learning (neural networks or SVMs), signal and image processing, sampling theory, statistics (kriging), response surface or surrogate modeling, finance, optimization. [email protected] MATH 590 – Chapter 1 5 Introduction
    [Show full text]
  • Engineering Theory and Mathematics in the Early Development of Information Theory
    1 Engineering Theory and Mathematics in the Early Development of Information Theory Lav R. Varshney School of Electrical and Computer Engineering Cornell University information theory in the American engineering community Abstract— A historical study of the development of information and also touch on the course that information theory took in theory advancements in the first few years after Claude E. Shannon’s seminal work of 1948 is presented. The relationship the American mathematics community. As the early between strictly mathematical advances, information theoretic development of information theory was being made, social evaluations of existing communications systems, and the meanings of the nascent field were just being constructed and development of engineering theory for applications is explored. It incorporated by the two different social groups, mathematical is shown that the contributions of American communications scientists and communications engineering theorists. The engineering theorists are directly tied to the socially constructed meanings constructed had significant influence on the direction meanings of information theory held by members of the group. The role played by these engineering theorists is compared with that future developments took, both in goals and in the role of American mathematical scientists and it is also shown methodology. Mutual interaction between the two social that the early advancement of information is linked to the mutual groups was also highly influenced by these social meanings. interactions between these two social groups. In the half century since its birth, Shannon information theory has paved the way for electronic systems such as compact discs, cellular phones, and modems, all built upon the I. INTRODUCTION developments and social meanings of its first few years.
    [Show full text]
  • English for It-Students Part Ii
    Куліш І.М., Рогульська А.B. ENGLISH FOR IT-STUDENTS PART II МІНІСТЕРСТВО ОСВІТИ І НАУКИ УКРАЇНИ ЧЕРКАСЬКИЙ НАЦІОНАЛЬНИЙ УНІВЕРСИТЕТ ІМЕНІ БОГДАНА ХМЕЛЬНИЦЬКОГО Куліш І.М., Рогульська А.В. ENGLISH FOR IT- STUDENTS PART II Черкаси - 2015 УДК 811. 111 (075.8) ББК 81. 2Ан – 91 К 90 Рецензенти: І.В. Некоз – кандидат педагогічних наук, доцент кафедри іноземних мов Черкаського національного університету ім. Б. Хмельницького I.Г. Багач . - канд.пед.наук, доц. кафедри романо-германської філології та перекладу Черкаського державного технологічного університету С.Р. Бабушко - канд.філ.наук, доц. кафедри української та іноземних мов Національного університету фізичного виховання і спорту України, м.Київ. Куліш І.М., Рогульська А.В. Англійська мова для студентів ІТ- спеціальностей: Навчальний посібник для студентів ІТ-спеціальностей. – Черкаси: Вид. від ЧНУ імені Богдана Хмельницького, 2015. – 109 с. Навчальний посібник сформований у відповідності до програми з іноземної мови за професійним спрямуванням для студентів 3 та 4 курсу ІТ- спеціальностей. Навчальний матеріал розташовано за тематичним принципом (за розділами). Робота за темою в межах одного розділу організовується на базі декількох основних текстів, зразків усного мовлення та завдань комунікативного характеру, текстів для додаткового читання, системи граматичних вправ репродуктивного та творчого характеру. Посібник вміщує індивідуальні творчі завдання для самостійної роботи студентів та вправи для контролю умінь та навичок студентів. Затверджено до друку на засіданні вченої ради Черкаського Національного університету імені Богдана Хмельницького протокол №3 від 14 грудня 2015 року ISBN 978-966-353-408-4 ЧНУ ім. Б.Хмельницького, 2015 Куліш І.М., Рогульська А.В., 2015 ПЕРЕДМОВА Навчальний посібник призначається для студентів 3 та 4 курсу ІТ- спеціальностей. Мета посібника – формувати у студентів навички читання та розуміння літератури фахової професійної тематики на основі активізації знань загальновживаної лексики та основ граматики.
    [Show full text]
  • Curso: Análisis Real II Clase 3: Aproximación De Funciones
    CONTENIDO REFERENCIAS SUGERIDAS CURSO:ANÁLISIS REAL II CLASE 3: APROXIMACIÓN DE FUNCIONES MEDIBLES POR FUNCIONES CONTINUAS Yamilet Quintana1 1Universidad Simón Bolívar Programa Interuniversitario de Doctorado en Matemáticas Junio, 2020 CONTENIDO REFERENCIAS SUGERIDAS 1 CONTENIDO Aproximación de funciones medibles por funciones continuas p Densidad de Cc(X) en L (X; µ), 1 ≤ p < 1 El teorema de Luzin 2 REFERENCIAS SUGERIDAS CONTENIDO REFERENCIAS SUGERIDAS 1 CONTENIDO Aproximación de funciones medibles por funciones continuas p Densidad de Cc(X) en L (X; µ), 1 ≤ p < 1 El teorema de Luzin 2 REFERENCIAS SUGERIDAS CONTENIDO REFERENCIAS SUGERIDAS APROXIMACIÓN DE FUNCIONES MEDIBLES POR FUNCIONES CONTINUAS Aproximación de funciones medibles por funciones continuas Para finalizar el Tema 1, en esta lección nos ocuparemos de dos resultados sobre aproximaxión de funciones: El teorema de densi- dad de las funciones continuas con soporte compacto en Lp(X; µ), 1 ≤ p < 1, y el teorema de Luzin sobre aproximación de funciones medibles por funciones continuas. Nuestro objetivo será enunciar y demostrar ambos resultados. CONTENIDO REFERENCIAS SUGERIDAS p DENSIDAD DE Cc (X) EN L (X; µ), 1 ≤ p < 1 p Densidad de Cc(X) en L (X; µ), 1 ≤ p < 1 TEOREMA 1-C3 Sean (X; τ) Hausdorff localmente compacto, B(X) su σ-álgebra de Borel, µ : B(X) ! [0; 1] regular, y 1 ≤ p < 1. Entonces Cc (X) es denso en Lp(X; µ). Demostración Seguiremos los enfoques de las referencias [2,10]. p Paso 1: Verifiquemos que Cc (X) es un subconjunto de L (X; µ). En efecto, si f 2 Cc (X) entonces f es acotada y Z p p p kf kLp(X,µ) = jf (x)j dµ(x) ≤ µ(supp(f )) kf k1 : X CONTENIDO REFERENCIAS SUGERIDAS p DENSIDAD DE Cc (X) EN L (X; µ), 1 ≤ p < 1 Demostración (cont.) Paso 2: Sea S el conjunto de las funciones simples que se anulan fuera de conjuntos de medida cero.
    [Show full text]
  • Stochastic Chemical Kinetics
    Stochastic Chemical Kinetics A Special Course on Probability and Stochastic Processes for Physicists, Chemists, and Biologists Summer Term 2011 Version of July 7, 2011 Peter Schuster Institut f¨ur Theoretische Chemie der Universit¨at Wien W¨ahringerstraße 17, A-1090 Wien, Austria Phone: +43 1 4277 527 36 , Fax: +43 1 4277 527 93 E-Mail: pks @ tbi.univie.ac.at Internet: http://www.tbi.univie.ac.at/~pks 2 Peter Schuster Preface The current text contains notes that were prepared first for a course on ‘Stochastic Chemical Kinetics’ held at Vienna University in the winter term 1999/2000 and repeated in the winter term 2006/2007. The current version refers to the summer term 2011 but no claim is made that it is free of errors. The course is addressed to students of chemistry, biochemistry, molecular biology, mathematical and theoretical biology, bioinformatics, and systems biology with particular interests in phenomena observed at small particle numbers. Stochastic kinetics is an interdisciplinary subject and hence the course will contain elements from various disciplines, mainly from probability theory, mathematical statistics, stochastic processes, chemical kinetics, evo- lutionary biology, and computer science. Considerable usage of mathemat- ical language and analytical tools is indispensable, but we have consciously avoided to dwell upon deeper and more formal mathematical topics. This series of lectures will concentrate on principles rather than technical details. At the same time it will be necessary to elaborate tools that allow to treat real problems. Analytical results on stochastic processes are rare and thus it will be unavoidable to deal also with approximation methods and numerical techniques that are able to produce (approximate) results through computer calculations (see, for example, the articles [1–4]).
    [Show full text]
  • Modelling Extreme Rainfall in the Era of Climate Change Concerns: Towards a Consistent Stochastic Methodology
    School for Young Scientists: “Modelling and forecasting of river flows and managing hydrological risks: towards a new generation of methods” Moscow, Russia, 22-26 October 2018 Modelling extreme rainfall in the era of climate change concerns: Towards a consistent stochastic methodology One Step Forward, Two Steps Back Demetris Koutsoyiannis Department of Water Resources and Environmental Engineering School of Civil Engineering National Technical University of Athens, Greece ([email protected], http://www.itia.ntua.gr/dk/) Presentation available online: http://www.itia.ntua.gr/1897/ Greetings from the Itia research team http://www.itia.ntua.gr/ D. Koutsoyiannis, Modelling extreme rainfall 1 Giants of the Moscow School of Mathematics D. Koutsoyiannis, Modelling extreme rainfall 2 On names and definitions: A contrast Ἀρχὴ παιδεύσεως ἡ τῶν ὀνομάτων ἐπίσκεψις” What’s in a name? That which (The beginning of education is the inspection of we call a rose, by any other names) name would smell as sweet. Attributed to Socrates by Epictetus, Discourses, Ι.17,12 William Shakespeare, “Romeo and Juliet” (Act 2, scene 2) Each definition is a piece of secret ripped from Let me argue that this Nature by the human spirit. I insist on this: any situation [absence of a complicated thing, being illumined by definitions, definition] ought not create being laid out in them, being broken up into concern and steal time from pieces, will be separated Into pieces completely useful work. Entire fields of transparent even to a child, excluding foggy and mathematics thrive for dark parts that our intuition whispers to us while centuries with a clear but acting, separating into logical pieces, then only evolving self-image, and can we move further, towards new successes due nothing resembling a to definitions .
    [Show full text]
  • Editorial Team European Mathematical Society
    CONTENTS EDITORIAL TEAM EUROPEAN MATHEMATICAL SOCIETY EDITOR-IN-CHIEF ROBIN WILSON Department of Pure Mathematics The Open University Milton Keynes MK7 6AA, UK e-mail: [email protected] ASSOCIATE EDITORS STEEN MARKVORSEN Department of Mathematics Technical University of Denmark Building 303 NEWSLETTER No. 34 DK-2800 Kgs. Lyngby, Denmark e-mail: [email protected] December 1999 KRZYSZTOF CIESIELSKI Mathematics Institute Jagiellonian University Reymonta 4 EMS News : Committee and Agenda .................................................................. 2 30-059 Kraków, Poland Editorial by EMS Secretary David Brannan ..................................................... 3 e-mail: [email protected] KATHLEEN QUINN Introducing the Editorial Team : Part 2 ........................................................... 7 Open University [address as above] EMS Executive meeting in Zurich ....................................................................... 8 e-mail: [email protected] Felix Klein Prize ............................................................................................... 10 SPECIALIST EDITORS 3ecm Barcelona: Second Announcement .......................................................... 12 INTERVIEWS Steen Markvorsen [address as above] EMS Poster Competition .................................................................................. 14 SOCIETIES EMS Council Meeting in Barcelona: Second Announcement ........................... 15 Krzysztof Ciesielski [address as above] Interviews - Jan van Maanen..........................................................................
    [Show full text]
  • Notes on the Poisson Point Process
    Notes on the Poisson point process Paul Keeler March 20, 2018 This work is licensed under a “CC BY-SA 3.0” license. Abstract The Poisson point process is a type of random object in mathematics known as a point process. For over a century this point process has been the focus of much study and application. This survey aims to give an accessible but detailed account of the Poisson point process by covering its history, mathematical defini- tions in a number of settings, and key properties as well detailing various termi- nology and applications of the point process, with recommendations for further reading. 1 Introduction In probability, statistics and related fields, a Poisson point process or a Pois- son process (also called a Poisson random measure or a Poisson point field) is a type of random object known as a point process that consists of randomly po- sitioned points located on some underlying mathematical space [51, 54]. The Poisson point process has interesting mathematical properties [51][54, pages xv- xvi], which has led to it being frequently defined in Euclidean space and used as a mathematical model for seemingly random objects in numerous disciplines such as astronomy [4], biology [62], ecology [84], geology [17], physics [74], im- age processing [10], and telecommunications [33]. For example, defined on the real line, it can be interpreted as a stochastic process 1 called the Poisson pro- cess [83, pages 7–8][2][70, pages 94–95], forming an example of a Levy´ process and a Markov process [73, page ix] [2]. In this setting, the Poisson process plays 1Point processes and stochastic processes are usually considered as different objects, with point processes being associated or related to certain stochastic processes [20, page 194][18, page 3][83, pages 7–8][25, page 580].
    [Show full text]
  • Golden Rotations
    GOLDEN ROTATIONS OLIVER KNILL Abstract. These are expanded preparation notes to a talk given on February 23, 2015 at BU. This was the abstract: "We look Pn k at Birkhoff sums Sn(t)=n = k=1 Xk(t)=n with Xk(t) = g(T t), where T is the irrational golden rotation and where g(t) = cot(πt). Such sums have been studied by number theorists like Hardy and Littlewood or Sinai and Ulcigrain [41] in the context of the curlicue problem. Birkhoff sums can be visualized if the time interval [0; n] is rescaled so that it displays a graph over the interval [0; 1]. While 1 for any L -function g(t) and ergodic T , the sum S[nx](t)=n con- verges almost everywhere to a linear function Mx by Birkhoff's ergodic theorem, there is an interesting phenomenon for Cauchy distributed random variables, where g(t) = cot(πt). The func- tion x ! S[nx]=n on [0; 1] converges for n ! 1 to an explicitly given fractal limiting function, if n is restricted to Fibonacci num- bers F (2n) and if the start point t is 0. The convergence to the \golden graph" shows a truly self-similar random walk. It ex- plains some observations obtained together with John Lesieutre and Folkert Tangerman, where we summed the anti-derivative G of g, which happens to be the Hilbert transform of a piecewise lin- ear periodic function. Recently an observation of [22] was proven by [40]. Birkhoff sums are relevant in KAM contexts, both in an- alytic and smooth situations or in Denjoy-Koksma theory which is a refinement of Birkhoff's ergodic theorem for Diophantine ir- rational rotations.
    [Show full text]